Question

Question 9 Task 28 v5

Your firm needs to invest in a new delivery truck. The life expectancy of the delivery truck is five years. You can purchase a new delivery truck for an upfront cost of $200,000, or you can lease a truck from the manufacturer for five years for a monthly lease payment of $4,100 (paid at the beginning of each month). Your firm can borrow at 8% APR with quarterly compounding.

a. Calculate the effective annual rate on your firm's borrowings.

b. Calculate the effective monthly discount rate that you should use to evaluate the truck lease.

c. What is the present value of the lease payments for the delivery truck?

d. Calculate the lease rate for which you would be indifferent between leasing and buying the truck.

e. Should you lease or buy?

(Hint: Do not round intermediate results from a. to d.)

a. The effective annual rate is %. (round to two decimals)

b. The effective monthly rate is %. (round to three decimals)

c. The PV of the lease is $. (round to full $)

d. The indifference lease rate is $. (round to full $)

e. (fill in "lease" or "buy")

Answer 1

Solution-

(A) Nominal rate applied quarterly is given as 8%

EAR = (1+8%/4)^4 - 1

= 8.243%

(B) Monthly effective rate is-

= (1+8%/4)^(1/3)-1

= 0.6623%

(C) PV of lease is calculated as follows-

We can use excel formula pv(0.00623,60,4100) = $202457

This gives PV of payments in arrear, however payments are in advance.

Thus we multiply this figure by 1.00623 to get PV = $203798

(D) Suppose lease rate is x

Then using excel goal seek we equate the empty cell so that the output of above given pv formula gives us PV equal to upfront cost of $200000

Hence, x = $4023.585 (monthly rent payment)

(E) As PV of lease at given rate is higher than the upfront cost, we should buy it now rather than leasing.

Thanks!